• Transactions of the Korean Society of Mechanical Engineers A
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• v.29 no.9 s.240
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• pp.1243-1252
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• 2005

A current trend of design methodologies is to make engineers objectify or automate the decision-making process. Numerical optimization is an example of such technologies. However, in numerical optimization, the uncertainties are uncontrollable to efficiently objectify or automate the process. To better manage these uncertainties, the Taguchi method, reliability-based optimization and robust optimization are being used. To obtain the target performance with the maximum robustness is the main functional requirement of a mechanical system. In this research, a design procedure for global robust optimization is developed based on the kriging and global optimization approaches. The DACE modeling, known as the one of Kriging interpolation, is introduced to obtain the surrogate approximation model of the function. Robustness is determined by the DACE model to reduce real function calculations. The simulated annealing algorithm of global optimization methods is adopted to determine the global robust design of a surrogated model. As the postprocess, the first order second-moment approximation method is applied to refine the robust optimum. The mathematical problems and the MEMS design problem are investigated to show the validity of the proposed method.

• Journal of Korean Society on Water Environment
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• v.22 no.5
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• pp.952-957
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• 2006

The present study applied wavelet transform and artificial neural networks (ANNs) for the prediction of daily TOC data. TOC data were transformed into denoised data by the wavelet transform and the noise-reduced data were used for the prediction model by artificial neural networks. For the application of wavelet transform, Daubechies wavelet of order 10 ('db10') was used as a basis function and decomposed the TOC data up to fifth level with five detail components and one approximation component. ANNs were calibrated with the input data of the segregated TOC data corresponding to the details from second to fifth level and the approximation. Consequently, the ANNs model for the prediction of daily TOC data showed the best result when it had seventeen hidden nodes in its layer.

• Journal of Korean Society of Coastal and Ocean Engineers
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• v.2 no.1
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• pp.51-57
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• 1990

Based on second-order Stokes wave and parabolic approximation, a refraction-diffraction model for linear and nonlinear waves is developed. With the assumption that the water depth is slowly varying, the model equation describes the forward scattered wavefield. The parabolic approximation equations account for the combined effects of refraction and diffraction, while the influences of bottom friction, current and wind have been neglected. The model is tested against laboratory experiments for the case of submerged circular shoal, when both refraction and diffraction are equally significant. Based on Boussinesq equations, the parabolic approximation eq. is applied to the propagation of shallow water waves. In the case without currents, the forward diffraction of Cnoidal waves by a straight breakwater is studied numerically. The formation of stem waves along the breakwater and the relation between the stem waves and the incident wave characteristics are discussed. Numerical experiments are carried out using different bottom slopes and different angles of incidence.

• Journal of Korean Society on Water Environment
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• v.23 no.4
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• pp.551-560
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• 2007

The present study analyzed noise reduction and long/short-term components for discharge, TOC concentration, and TOC load data in order to understand the data characteristics better. For the purpose, wavelet transform which can reduce noise from raw data and has flexible resolution in time and frequency domain was applied and the theory of nonlinear dynamics was also used to determine the last decomposition level for wavelet transform. Wavelet function of 'db10' and the 7th level for the last decomposition of wavelet transform were applied for the all data in the present study. Also the results revealed that the energy ratios of approximation components with 187-hour periodicity decomposed from 7th level of wavelet transform were 94.71% (discharge), 99.00% (TOC concentration), and 93.84% (TOC load), respectively. In addition, the energy ratios of detail components showed the range between 1.00% and 6.17%, which were extremely small comparing to the energy ratios of approximation components, therefore, the first and second detail components might be considered as noise components included in the raw data.

• Transactions of the Korean Society of Mechanical Engineers A
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• v.20 no.12
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• pp.3804-3821
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• 1996

The configuration optimization is a structural optimization method which includes the coordinates of a structure as well as the sectional properties in the design variable set. Effective reduction of the weight of discrete structures can be obrained by changing the geometry while satisfying stress, Ei;er bickling, displacement, and frequency constraints, etc. However, the nonlinearity due to the configuration variables may cause the difficulties of the convergence and expensive computational cost. An efficient approximation method for the configuration optimization has been developed to overcome the difficulties. The method approximates the constraint functions based onthe second-order Taylor series expansion with reciprocal design variables. The Hessian matrix is approzimated from the information on previous design points. The developed algotithms are coded and the examples are solved.

• Structural Engineering and Mechanics
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• v.50 no.5
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• pp.679-695
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• 2014

A design method of second generation wavelet (SGW)-based multivariable finite elements is proposed for static and vibration beam analysis. An important property of SGWs is that they can be custom designed by selecting appropriate lifting coefficients depending on the application. The SGW-based multivariable finite element equations of static and vibration analysis of beam problems with two and three kinds of variables are derived based on the generalized variational principles. Compared to classical finite element method (FEM), the second generation wavelet-based multivariable finite element method (SGW-MFEM) combines the advantages of high approximation performance of the SGW method and independent solution of field functions of the MFEM. A multiscale algorithm for SGW-MFEM is presented to solve structural engineering problems. Numerical examples demonstrate the proposed method is a flexible and accurate method in static and vibration beam analysis.

• Journal of the Chungcheong Mathematical Society
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• v.20 no.4
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• pp.419-432
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• 2007

Double-diffusive convection inside a triangular porous cavity is studied numerically. Galerkin finite element method is adopted to derive the discrete form of the governing differential equations. The first-order backward Euler scheme is used for temporal discretization with the second-order Adams-Bashforth scheme for the convection terms in the energy and species conservation equations. The Boussinesq-Oberbeck approximation is used to calculate the density dependence on the temperature and concentration fields. A parametric study is performed with the Lewis number, the Rayleigh number, the buoyancy ratio, and the shape of the triangle. The effect of gravity orientation is considered also. Results obtained include the flow, temperature, and concentration fields. The differences induced by varying physical parameters are analyzed and discussed. It is found that the heat transfer rate is sensitive to the shape of the triangles. For the given geometries, buoyancy ratio and Rayleigh numbers are the dominating parameters controlling the heat transfer.

• Transactions of the Korean Society of Mechanical Engineers A
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• v.22 no.4
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• pp.811-825
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• 1998

An approximate line search is presented for dynamic response optimization with Augmented Lagrange Multiplier(ALM) method. This study empolys the approximate a augmented Lagrangian, which can improve the efficiency of the ALM method, while maintaining the global convergence of the ALM method. Although the approximate augmented Lagragian is composed of only the linearized cost and constraint functions, the quality of this approximation should be good since an approximate penalty term is found to have almost second-order accuracy near the optimum. Typical unconstrained optimization algorithms such as quasi-Newton and conjugate gradient methods are directly used to find exact search directions and a golden section method followed by a cubic polynomial approximation is empolyed for approximate line search since the approximate augmented Lagrangian is a nonlinear function of design variable vector. The numberical performance of the proposed approach is investigated by solving three typical dynamic response optimization problems and comparing the results with those in the literature. This comparison shows that the suggested approach is robust and efficient.

• Journal of Ocean Engineering and Technology
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• v.28 no.4
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• pp.324-330
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• 2014

In this study, the numerical model developed by Hong et al.(2008) was improved to be applied to rapidly varying flows such as the inundation of dry land or flow transitions due to large gradients of the bathymetry. A numerical approximation was applied that was consistent with the conservation of momentum in flow expansions and with the Bernoulli equation in flow contractions. The approximation was second order, but the accuracy reduced to first order near extreme values by the use of a minmod limiter. The modified model was verified by acomparison with the theoretical critical depth of weir, and for sufficiently smooth conditions and a fine grid size, both approximations converged to the same solution. In terms of the grid size, it was more effective at obtaining solutions than the previous model and reproduced the inundation of dry land.

• Journal of applied mathematics & informatics
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• v.31 no.5_6
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• pp.609-621
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• 2013

At present, research on providing new methods to solve nonlinear integral equations for minimizing the error in the numerical calculations is in progress. In this paper, necessary conditions for existence and uniqueness of solution for nonlinear 2D Fredholm integral equations are given. Then, two different numerical solutions are presented for this kind of equations using 2D shifted Legendre polynomials. Moreover, some results concerning the error analysis of the best approximation are obtained. Finally, illustrative examples are included to demonstrate the validity and applicability of the new techniques.